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Tracking algorithms for the active target MAYA T. Rogera,b,∗, M. Caamanõc, C.E. Demonchyd, W. Mittige, H. Savajolsa, I. Tanihataf aGANIL, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 05, France 1 bInstituut voor Kern-en Stralingsfysica, K.U. Leuven, Celestijnenlaan 200D, B-3001 1 Leuven, Belgium 0 cUniversidade de Santiago de Compostela, E-15786 Santiago,, Spain 2 dCENBG-UniversitBordeaux 1-UMR 5797 CNRS/IN2P3, Chemin du Solarium, BP 120, F-33175 Gradignan Cedex, France n eNSCL, MSU, East Lansing, Michigan 48824, USA a fRCNP, Osaka University, Mihogaoka, Ibaraki, Osaka 567 0047, Japan J 9 1 ] x Abstract e - l TheMAYAdetectorisaTime-ChargeProjectionChamberbasedontheconcept c u of active target. These type of devices use a part of the detection system, the n [ filling gas in this case, in the role of reaction target. The MAYA detector 2 performsthree-dimensionaltracking,inordertodeterminephysicalobservables v 0 of the reactions occurring inside the detector. The reconstruction algorithms 6 of the tracking use the information from a two-dimensional projection on the 5 3 segmented cathode, and, in general, they need to be adapted for the different . 2 experimental settings of the detector. This work presents some of the most 1 0 relevant solutions developed for the MAYA detector. 1 : v Keywords: Active target, Gaseous detector, Trajectory reconstruction, i X Tracking algorithm, Simulation r a PACS: 29.85.Fj, 29.40.Gx, 29.40.Cs 1. Introduction Nowadays,thedevelopmentofnewradioactivebeamsallowsnuclearphysics to explore more exotic regions of the nuclear chart, revealing more new prop- ∗Correspondingauthor Email address: [email protected] (T.Roger) Preprint submitted toNuclear Instruments and Methods A January 20, 2011 erties as they become experimentally available. The access to these regions usuallyinvolveexotic withlow intensity andreactionswith smallcross-sections thatforce to improvedetection andanalysistechniques. To overcomethese dif- ficulties,experimentalsetupsfocusondifferentsolutions,suchashighefficiency and signal-to-noise discrimination, and the use of thick targets. Active target detectors, i.e, detection devices that use part of their systems as reaction target, proved to match these needs: since the detection is done inside the target, detection efficiency and effective target thickness are increased without losing resolution due to reaction point indetermination. The concept of active target, developed more than fifty years ago in high- energyphysicsuses,is beingprogressivelyadaptedforits applicationinnuclear physics. Thearchetypeofactivetargetsinthedomainofsecondarybeamsisthe detector IKAR [1], used at GSI (Germany) to study elastic scattering of exotic beams at relativistic energies. Another example is the MSTPC detector [2] designedatRIKEN(Japan)tostudy fusionandastrophysicalnuclearreactions in low-energy regions. Presently, new designs are mostly based on gas-filled devices where the gas constitutes both the target and the detection medium. Among these, MAYA [3, 4], developed and built at GANIL, is designed to explore very low energy domains not accessible with the use of solid or liquid targets. TheMAYAdetectorappliestheconceptofChargeandTimeProjection toperformafull three-dimensionalreconstructionofthe detectedreactionwith the charge collected in a segmented cathode and its associated drift time. Most of the active targets in development use a similar configuration, with the tracking performed on a segmented layer. Therefore, some of the problems and solutions that appear in the reconstruction process are common to these detectors. In the case of MAYA, the tracking process needs to be adapted to the experimental configurations used to study different reactions, producing a collectionofreconstructionprotocolstoextracttherelevantobservables. Among these, the angle, reaction vertex, and stopping points need specific formulas to be determined. Here, the most significant of these algorithms are reviewed. 2 charged particles _ Ancillary detectors e 28 cm isobutane 20 cm Frish grid Amplification wires Segmented cathode Beam 25 cm Figure1: (Coloronline)ThepictureshowsaschematicrenditionoftheMAYAactive-target. Abeam projectileenters the detector volumewhereitreacts withanucleus inthegas. The particles involved in the reaction may produce enough ionization to induce a pattern in the segmentedcathode,aftertraversingaFrischgridandaplaneofamplificationwires. Asetof ancillarydetectors isusedintheexitsideofthedetector. 2. The MAYA Detector Figure 1 shows a typical MAYA setup. Two main zones can be identified within the detector: an active volume of 28×26×20 cm3 where the reaction takesplace,andthe amplificationareawheredetectionandreadoutoccur. The amplification zone consists of a Frisch grid, an anode wire plane below, and a segmented cathode in the lower part. The cathode is segmented into 33×32 hexagonalpads,eachofwhichmeasures5mmperside,arrangedinrowsparallel to the anode wires. In general, the detection occurs when the beam particles and the reaction products ionize the filling gas along their paths. The electrons released in the ionizationprocessdrifttowardtheamplificationareawheretheyareaccelerated 3 in the vicinity of the wires, inducing mirror chargeson the correspondingpads, which are measured and coded individually. Typically, the image charge from one avalanche will spread over several pads and the resulting distributions are used to obtain a two dimensional projection of the tracks of charged particles. Measurementsofthe drift time ofthe ionizing electronsup to the amplifica- tionwiresallowtocalculatethe verticalposition. Thisinformationiscombined withthereconstructionoftrajectoriesprojectedonthecathodeplanetoperform acomplete3-dimensionaltrackingofthereactionproductsthatloseenoughen- ergy to be detected. Ancillary detectors, such as cesium iodide crystals [5], silicon [6–8], or diamond detectors are usually placed at the back, correspond- ingto forwardanglesinorderto detectparticlesthatdo notstopinsidethe gas volume. Also, stoppers are employed for non-reacting beam particles that do not stop in the filling gas. Other modifications include beam-shielding [6] and a modified drift chamber placed before the ancillary detectors. The filling gasis chosenaccordingto the reactionofinterest. So far,MAYA was operated and tested with 2H or 4He, either pure or mixed with standard 2 detection gases such as methyl-propane C H or CF , at pressures between 4 10 4 20 mbar and 1 atm. The trajectory reconstruction from the sampled positions in the segmented cathode requires different algorithms that may vary from one configuration to theother. Thetrackingtechniquesextractinformationsuchasprojectedangles oftrajectories,the positionofthe reactionvertex,andthe determinationofthe stopping points, which are necessary to determined the range of the particles inside the gas. 3. Two-Dimensional Charge Distributions The two-dimensional projection of the particle trajectories on the cathode plane can be described as the convolution of different processes: the ionization pathis digitizedperpendicularlytothe beamdirectionasthe releasedelectrons are attracted to the amplification wires; the amplification process induces a 4 Ionizing particle Induced charge Drift electrons Amplification wires Ionizing Pads Induced particle charge Amplification wires Pads Figure 2: The processes involved in the formation of the two-dimensional pattern in the cathodeplaneareschematicallysummarizedinthepicture. Leftdrawingisaverticalscheme oftheionization,digitalization,andchargeinduction. Rightfigureshowsthesameprocesses inthehorizontalplane. mirrorchargeonthepadsbelowthewiresthatcanbedescribedasproducedby multiplepoint-likesources;theseareweightedbytheenergy-lossoftheparticles; and finally the resulting induced charge is integratedin the hexagonal-shapeof each pad. Fig. 2 summarizes these processes. These steps are reproduced in a simulation of the entire process, providing realistic patterns where different algorithmscanbetestedtoreconstructtheoriginaltracks. Thesimulationcode generates two-dimensional patterns by reproducing the different processes: -Theenergy-lossalongtheparticletrajectoryfordifferentionizingparticles, energies, and gas compositions and pressures is obtained from Monte Carlo simulations using the TRIM code [13]. A typical energy-lossprofile of a 2 MeV proton in 1 atm of isobutane is presented in Fig. 3. The calculated energy- loss profiles are projected (digitized) along the wires to determine the total chargeinduced, Q in Eq. 1, by each point-like source along the trajectory. The straggling of the electrons inside the gas is not yet included. For E/P > 0.8 V.cm−1.Torr−1, it has been estimated to be less than 1 mm. - The induction from a point-like source can be expressed as an exact elec- trostatic formula, as it is shown in Ref. [9]: 5 1.5 m)30 s) m nit V/ arb. u 1 s (ke20 harge (0.5 ergy los10 C n E 0 0 0 10 20 30 40 0 100 200 Position (mm) Depth (mm) Figure 3: Left panel: Simulated charge distribution created by a point source along one dimension (solid line), integrated over pads (dashed line). The distribution corresponds to L=10cm inEq. 1. Rightpanel: Energy-losscurveofa2MeVprotonin1atmof isobutane generatedbytheTRIMcode. −Q ∞ (−1)n(2n+1)L σ(x,y)= (1) 2π [(2n+1)2L2+x2+y2]3/2 n=0 X where Q is the total charge, L is the distance between the point-like source and the observation plane, and x,y is the position with respect to the source. A typical charge distribution created by a point-like source is shown in Fig. 3. - Finally, the charge-induced distributions from all point-like sources is integrated on the surface of each pad to obtain the charge measured. The reconstruction algorithms are tested on sets of data that reproduce different experimental conditions in MAYA. These are classified depending on the particles detected on the cathode as: - Single-track setups tag those where beam particles do not produce any charge pattern on the cathode plane, either because its energy-loss is too small (see for example [5]), or because electrons created by the incident ions are stopped before reaching the amplification stage (see [6]). - Multi-tracksetups refertoconfigurationswhere bothbeamandrecoilpar- ticles contribute to the recorded pattern (as in [8]). Examples of charge distri- 6 200 200 m) m) 150 150 m m (A (A Y Y A100 A100 M M Y Y 50 50 0 0 0 100 200 0 100 200 X (mm) X (mm) MAYA MAYA Figure 4: (Color online) Two-dimensional projection of the charge distribution measured froma1H(11Li,9Li)treactionin150mbarofisobutane(leftpanel)andfroma13Nnucleusof 8.7MeVin30mbarofisobutaneproducedinthe12C(8He,13N)7Hreaction[10](rightpanel) butions measured in such cases are presented in Fig. 4. 4. Trajectory Reconstruction In a first stage, the data analysis aims at extracting the direction of the trajectories from the induced patterns. However, no universal tracking algorithm can be used to reconstruct all the different types of pattern found in the experiments performed. Two basic methods, referred as the Hyperbolic Secant Squared and the Global Fitting methods, proved to be useful in most of the cases. They are reviewed in the following sections. 4.1. The Hyperbolic Secant Squared method The Hyperbolic Secant Squared (SECHS) method is based on the determi- nation and selection of the intersection points of the particle trajectory with the three symmetry axis of the cathode, defined by the hexagonal shape of the pads (see Fig. 5). The selected points are used to fit a straight line, which corresponds to the projected trajectory of the particles. 7 Figure5: Illustrationofthealgorithmusedtochoosetheoptimumaxisforthereconstruction of the track. In the picture, it corresponds to the axis labeled as “axis 2”, which yields the highestnumberofmaximafound. The first step is to identify the maxima of the collected charge, i.e. the highest charge with two non-zero neighboring charges, along each symmetry axis. Figure5showsthesearchofmaximaoveranexperimentaltrackmeasured inRef. [5]. Oncethepadswithmaximumchargeareidentified,the intersection point is estimated from the position of the pad and the centroid of the charge distributed between the pad and its two immediate neighbors. This is done using the SECHS formula [11] in a modified version [3]: ∆ = w ln 11−+aa11 (2) R 2 ln a +(cid:16) a2(cid:17)−1 2 2 (cid:16) p (cid:17) Q0 − Q0 with a = Q+ Q− and a = 1 Q0 + Q0 1 q2sinhqa2 2 2 sQ+ sQ−! where∆ isthedistancebetweentheestimatedpositionofthecentroidandthe R center of the pad with the maximum charge, Q0. Q+ and Q− are the charges measured on the left and right neighboring pads, and w is the pad width. The particle trajectory, i.e. its projected angle and position, are then fitted from 8 Beam Heavy 200 ) m 150 m ( A Y A100 M Y 50 Light 0 0 100 200 X (mm) MAYA Figure 6: (Color online) Separation of the cathode plane in three different zones used to reconstructthetrajectoriesofthedifferentchargedparticles. the resulting centroids, separately for each symmetry axis. In order to avoid heavy data processing, the symmetry axis with the highest number of maxima was chosen to follow the whole method in some of the previous analysis (see Fig. 5). Another adaption of this process consists in the definition of different areas of search when there are multiple particles involvedin the reaction. For single- tracksetups, the searchis performedoverthe whole cathode plane, whereasfor multi-track setups different areas that encompass each individual track have to be considered. Usually, the beam track is separatedfrom the reactionproducts dividingthecathodeplaneintothreeareasalongthebeamaxis,asshowninFig. 6. Other division patterns may be applied depending on the particles detected in the cathode. 9 Theangularresolutionofthismethoddependsstronglyontheanglebetween the trajectory and the symmetry axis. The simulated resolution in single-track setups ranges between 0 deg for trajectories perpendicular to any of the symmetry axis (i.e. trajectories with 30, 90, or 150 deg respect to the beam line), and 1 deg for those parallel(i.e. trajectories with 0, 60 or 120 deg. The reason forthisdifferenceisillustratedinFig. 7: whenapproachingtheendofthetrack the reconstructedmaximaofchargedeviate fromthe trajectory,the chargedis- tribution along the chosen symmetry axis being not described by the SECHS functionanymore,producingshiftedcentroids,andintroducingasystematicer- rorinthe fitting process. This effectcanbereducedwithacombineduseofthe centroidsfrommorethanonesymmetryaxis,thisapproachincreasestheresolu- tionandreducesthe errorto less than0.5deg (see Fig. 8). Another possibility, ifthe trackislongenough,istoexcludethesepoints,whichcorrespondapprox- imately to the two first and two last centroids in the case of the single-track setups,andthe twolastonesforthe multi-tracksetups. Thisoperationreduces the uncertainty to less than 0.2 deg (see Fig. 8). For multi-track setups, only the endofthe trackisavailableandthereforethe effectofthe shifting centroids is diminished. In these situations, the uncertainty is reduced approximately in a factor two, compared to the single-track setups. 4.2. The Global Fitting method TheuseoftheSECHSmethodrequiresthepresenceofmaximainthecharge pattern. However, this is not always the case. In reactions involving light particles with relatively high energy, the charge induced is not spread enough overthe pads, due to the energy-lossprofile of such particles. In this particular case,adifferentmethodisused,basedonafitofthewholechargedistributionby means of the orthogonal distance regression procedure [12]. This method aims at finding the parameters of a first-degree polynomial minimizing the value of: N (a x +a −y )2 χ2 = Q 0 n 1 n (3) n a2+1 n=0 0 X 10